About 40 years ago, the critic Roland Barthes wrote an essay called The Death of the Author. This made a call for a new way of reading. Let us approach a piece of writing without any thought of its writer. Let us read freely. The attempt to extract any authoritative meaning from a text is futile. The myth of authorship, with its appeal to history, biography, psychology, should be thrown out. "The birth of the reader must be at the cost of the death of the Author."

What this celebrated manifesto really says, whether its arguments work, are open to doubt. But its title is suggestive. It can raise matters and problems of a more practical nature. There are, after all, many literally authorless works. And there are works that suddenly lose their authors.

Barthes was a literary man. It is quite rare for a piece of literature, having once had one, to be deprived of its author. But in the world of art, authors are always dying off. Works that were previously assigned to a known name, works that were among the most famous, find themselves stranded in anonymity. The process is called de-attribution.

Examples? Recently two classic works have been cut loose from their established makers. At the start of this year, the Prado declared The Colossus to be no longer Goya's. The painting of the figures in the valley indicated an inferior hand. It was probably his assistant Asensio Juliá, though that is not yet ascertained.

And a few years ago, Scotland's finest, The Skating Minister (The Reverend Robert Walker Skating on Duddingston Loch), was removed from Henry Raeburn and ascribed to a French painter, Henri-Pierre Danloux. Danloux is thought to have been working in Edinburgh in the 1790's, and is arguably a more likely-looking candidate.

Neither case is settled. The Colossus remains within the circle of Goya. If this painting has the marks of his genius, and it obviously does, then the spirit of Goya was doubtless around at its making. Its fearful and sublime idea, the pugilist giant rising up behind the world, could have been one of the master's ideas. Even though its authorship stays unsure, it won't be straying far from Goya.

The Skating Minister is in a different pickle. It really is unlike any other work by Raeburn. But it's miles better than any other work by Danloux. In its teetering balance between stasis and speed, between dignity and absurdity, it creates a work of high comedy that's rare in painting anywhere. It's a work of genius – but whose? It lingers, for the moment, in an uneasy limbo: a marvellous painting that has, in effect, arrived from nowhere. It will be a long time before people give up on finding it an author.

But there are works whose anonymity is firmly accepted. One of these is a painting called A Dead Soldier. It had an author once, a very distinguished one. When it turned up in Paris at the start of the 19th century it was credited to Velazquez. Manet thought it was by Velazquez when he based the figure of The Dead Toreador on it. It was still a Velazquez when the National Gallery bought it in 1865. Soon there were doubts.

Since then its origin has been disputed. It's been ascribed to various 17th-century artists and schools from both Spain and Italy. Currently, it's just labelled as 17th Century, Italian – maybe Neapolitan. That needn't be final. One day the answer may emerge, and some people would prefer that. But this picture has lived for a long time without a signature.

Its anonymity is provoking. It is a striking and mysterious image. A man in black armour lies dead beneath a tree, but his death has no visible story. Who can have invented the flat-out, obliquely-angled supine pose that inspired Manet? And how did this artist devise this strange, hybrid genre?

Notionally we see a dead body on the battlefield. But it's set about with formal emblems of death from a vanitas scene – skull and bones, bubbles bubbling in a foreground pool, a smoking lamp dangling from a branch. The human corpse becomes one more symbolic prop among others. Whoever came up with this picture is evidently an artist worth knowing more of.

No work comes out of the air. A Dead Soldier had an artist behind it, though now unknown, and we can presume it wasn't their only work. The picture is part of an oeuvre, and if we knew this oeuvre, and the wider scene that the artist belonged to, we could fit this picture solidly into its context. It would acquire a fixed coordinate point in the world.

So does an anonymous work make the viewer freer? Does ignorance let us look without limits? Perhaps. But the unknown also exerts a mystique. You can currently see A Dead Soldier in an exhibition at the Hayward Gallery. It's called "The Russian Linesman", and is curated by the artist Mark Wallinger. It's a show devoted to borderline cases. A Dead Soldier is here as a case of anonymity conferring uniqueness.

As Wallinger remarks, the authorless work becomes a one-off. "One expects a loss of charisma to occur when a work is demoted to 'school of' or, worse still, when even its country of origin is in doubt. But adrift from the structural certainties of time and place the unattributed gain a curious singularity: they are the only one of their species."

Or you could see A Dead Soldier as like The Unknown Warrior. As the inscription on his tomb in Westminster Abbey says: BENEATH THIS STONE RESTS THE BODY OF A BRITISH WARRIOR UNKNOWN BY NAME OR RANK BROUGHT FROM FRANCE TO LIE AMONG THE MOST ILLUSTRIOUS OF THE LAND.

He's famous and faceless. He's a magical figure because he could be anyone.

'A Dead Soldier' is currently on display in The Russian Linesman, the Mark Wallinger-curated exhibition at the Hayward Gallery, London, until 4 May. It then tours to Leeds Art Gallery (0113 247 8256) 16 May to 28 June; Glynn Vivian Art Gallery, Swansea (01792 516 900) 18 July to 20 September